My headcanon:
Solidifying real water into real ice, or melting real ice back into real water, I think would simply require lowering or raising its temperature, which should be relatively easy to do with normal ninjutsu/fuuinjutsu. Consider Jiraiya's Finger Carving Seal, which wasn't a fire nature jutsu but still allowed him to heat up his fingertip in order to burn a message into a surface. I'm pretty sure you could make a wide area-of-effect version of that jutsu and use it to melt a large amount of ice/snow. Doing the reverse and lowering the temperature of the water with normal chakra shouldn't be much more difficult.
If you wanted to infuse that water with chakra and telekinetically throw it around afterward then yeah, you would still need water natured chakra. Likewise, you would need Ice Release if you wanted to weaponize some ice that you just created. But simply melting the ice/snow into water or vice/versa could be done with normal chakra.
Edit: Although I suspect that it's probably possible to manipulate soft snow to a limited degree with Water Release since it still has some fluidity to it and is more similar to water than to solid ice. This I think would work similar to how Kankuro used sand to disguise his puppet during the chuunin exam despite not being Shukaku's jinchuuriki (I assume he used an earth release jutsu.) You wouldn't be able to control the snow effectively enough to weaponize it, but you could probably tunnel and/or swim through a snow drift, or make a cool snowman, or have an awesome snowball fight.
Edit 2: I random thought I just had. You could probably create cool ice sculptures without the Ice Release Bloodline by using teamwork. One ninja would use Water Release to shape a puddle of water into the desired shape and hold it still, while another uses a non-elemental cooling jutsu to lower the water's temperature and freeze it solid.